Quantum Gravitational Collapse Research Articles

On the Generalized Lemaitre Tolman Bondi Metric: Classical Sensitivities and Quantum Einstein‐Vaz Shells

AbstractIn this paper, in the classical framework, the lower bounds for the sensitivities of the generalized Lemaitre Tolman Bondi metric are evaluated. The calculated lower bounds via the linear dynamical systems , , and are , and respectively. The sensitivities and the lower sensitivities via are zero are also shown. In the quantum framework, the properties of the Einstein‐Vaz shells which are the final result of the quantum gravitational collapse arising from the Lemaitre Tolman Bondi discussed by Vaz in 2014 are analyzed. In fact, Vaz showed that continued collapse to a singularity can only be obtained if one combines two independent and entire solutions of the Wheeler‐DeWitt equation. Forbidding such a combination leads naturally to matter condensing on the Schwarzschild surface during quantum collapse. In that way, an entirely new framework for black holes (BHs) has emerged. The approach of Vaz was also consistent with Einstein's idea in 1939 of the localization of the collapsing particles within a thin spherical shell. Here, following an approach of oned of us (CC), we derive the BH mass and energy spectra via a Schrodinger‐like approach, by further supporting Vaz's conclusions that instead of a spacetime singularity covered by an event horizon, the final result of the gravitational collapse is an essentially quantum object, an extremely compact “dark star”. This “gravitational atom” is held up not by any degeneracy pressure but by quantum gravity in the same way that ordinary atoms are sustained by quantum mechanics. Finally, the time evolution of the Einstein‐Vaz shells is discussed.

Black Hole Spectra from Vaz's Quantum Gravitational Collapse

AbstractIn 2014, in a famous paper Hawking strongly criticized the firewall paradox by claiming that it violates the equivalence principle and breaks the CPT invariance of quantum gravity. He proposed that the final result of the gravitational collapse should not be an event horizon, but an apparent horizon instead. On the other hand, Hawking did not give a mechanism for how this could work. In the same year, Vaz endorsed Hawking's proposal in a quantum gravitational model of dust collapse by winning the Second Prize in the 2014 Gravity Research Foundation Essay Competition. He indeed showed that continued collapse to a singularity can only be obtained if one combines two independent and entire solutions of the Wheeler‐DeWitt equation. Vaz's interpretation of the paradox was in terms of simply forbidding such a combination. This leads naturally to matter condensing on the apparent horizon during quantum collapse. In that way, an entirely new framework for black holes (BHs) has emerged. The approach of Vaz was also consistent with Einstein's idea in 1939 of the localization of the collapsing particles within a thin spherical shell. In this work we derive the BH mass and energy spectra via a Schrodinger‐like approach, by further supporting Vaz's conclusions that instead of a spacetime singularity covered by an event horizon, the final result of the gravitational collapse is an essentially quantum object, an extremely compact “dark star”. This “gravitational atom” is held up not by any degeneracy pressure but by quantum gravity in the same way that ordinary atoms are sustained by quantum mechanics. Finally, by evoking the generalized uncertainty principle, the maximum value of the density of Vaz's shell will be estimated.

Quantum Gravity of Dust Collapse: Shock Waves from Black Holes.

We study the quantum gravitational collapse of spherically symmetric pressureless dust. Using an effective equation derived from a polymer quantization in the connection-triad phase space variables of general relativity, we find numerically, for a variety of initial dust configurations, that (i)trapped surfaces form and disappear as an initially collapsing density profile evolves into an outgoing shock wave; (ii)black hole lifetime is proportional to the square of its mass; and (iii)there is no mass inflation at inner apparent horizons. These results provide a substantially different view of black hole formation and subsequent evolution than found from semiclassical analyses.

Quantization of Gravitationally Bound Systems

Some of the approaches to quantization in gravity theory concerning gravitationally bound systems are considered. Grades of quantization applicable to these systems have been classified in terms of quantum mechanics, quantum field theory, and quantum geometrodynamics. Energy levels for the graviatom, Lemaître’s atom, quantum gravitational collapse have been calculated, and relationships for the masses of bound system components, as well as Universe’s birth probabilities, are presented to exemplify the properties of gravitationally bound systems. Objects and processes in them have been analyzed to construct quantum models of compact astrophysical objects and the early Universe.

Quantum gravitational collapse as a Dirac particle on the half line

We show that the quantum dynamics of a thin spherical shell in general relativity is equivalent to the Coulomb-Dirac equation on the half line. The Hamiltonian has a one-parameter family of self-adjoint extensions with a discrete energy spectrum $|E| < m$, and a continuum of scattering states for $|E|>m$, where $m$ is the rest mass of the shell and $E$ is the Arnowitt-Deser-Misner mass. For sufficiently large $m$, the ground state energy level is negative. This suggests that classical positivity of energy does not survive quantization. The scattering states provide a realization of singularity avoidance. We speculate on the consequences of these results for black hole radiation.

Quantum collapse of a charged n-dimensional BTZ-like domain wall

We investigate both the classical and quantum gravitational collapse of a massive, charged, nonrotating [Formula: see text]-dimensional Bañados–Teitelboim–Zanelli (BTZ)-like domain wall in AdS space. In the classical picture, we show that, as far as the asymptotic observer is concerned, the details of the collapse depend on the amount of charge present in the domain wall; that is, if the domain wall is extremal, nonextremal or overcharged. In both the extremal and nonextremal cases, the collapse takes an infinite amount of observer time to complete. However, in the over-charged case, the collapse never actually occurs, instead one finds an oscillatory solution which prevents the formation of a naked singularity. As far as the infalling observer is concerned, in the nonextremal case, the collapse is completed within a finite amount of proper time. Thus, the gravitational collapse follows that of the typical formation of a black hole via gravitational collapse.Quantum mechanically, we take the absence of induced quasi-particle production and fluctuations of the metric geometry; that is, we ignore the effect of radiation and back-reaction. For the asymptotic observer, we find that, near the horizon, quantization of the domain wall does not allow the formation of the black hole in a finite amount of observer time. For the infalling observer, we are primarily interested in the quantum mechanical effect as the domain wall approaches the classical singularity. In this region, the main result is that the wave function exhibits nonlocal effects, demonstrated by the fact that the Hamiltonian depends on an infinite number of derivatives that cannot be truncated after a finite number of terms. Furthermore, in the large energy density limit, the wave function vanishes at the classical singularity implying that quantization does not rid the black hole of its singularity.

Quantum gravitational dust collapse does not result in a black hole

Quantum gravity suggests that the paradox recently put forward by Almheiri et al. (AMPS) can be resolved if matter does not undergo continuous collapse to a singularity but condenses on the apparent horizon. One can then expect a quasi-static object to form even after the gravitational field has overcome any degeneracy pressure of the matter fields. We consider dust collapse. If the collapse terminates on the apparent horizon, the Misner–Sharp mass function of the dust ball is predicted and we construct static solutions with no tangential pressure that would represent such a compact object. The collapse wave functions indicate that there will be processes by which energy extraction from the center occurs. These leave behind a negative point mass at the center which contributes to the total energy of the system but has no effect on the energy density of the dust ball. The solutions describe a compact object whose boundary lies outside its Schwarzschild radius and which is hardly distinguishable from a neutron star.

Modified general relativity as a model for quantum gravitational collapse

We study a class of Hamiltonian deformations of the massless Einstein–Klein–Gordon system in spherical symmetry for which the Dirac constraint algebra closes. The system may be regarded as providing effective equations for quantum gravitational collapse. Guided by the observation that scalar field fluxes do not follow metric null directions due to the deformation, we find that the equations take a simple form in characteristic coordinates. We analyze these equations by a unique combination of numerical methods and find that Choptuik’s mass scaling law is modified by a mass gap as well as jagged oscillations. Furthermore, the results are universal with respect to different initial data profiles and robust under changes of the deformation.

Time and a Physical Hamiltonian for Quantum Gravity

We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach.

Quantum gravitational collapse in the Lemaitre–Tolman–Bondi model with a positive cosmological constant

Previous papers dealt with the quantization of the Lemaître–Tolman–Bondi (LTB) model for vanishing cosmological constant Λ. Here we extend the analysis to the case Λ > 0. Our main goal is to present solutions of the Wheeler–DeWitt equation, to give their interpretation and to derive Hawking radiation from them. We restrict ourselves to a discussion of those points that are different from the Λ = 0-case. These are mainly to do with the occurrence of two horizons.

Quantum radiation from quantum gravitational collapse

We study quantum radiation emitted during the collapse of a quantized, gravitating, spherical domain wall. The amount of radiation emitted during collapse now depends on the wavefunction of the collapsing wall and the background spacetime. If the wavefunction is initially in the form of a sharp wavepacket, the expectation value of the particle occupation number is determined as a function of time and frequency. The results are in good agreement with our earlier semiclassical analysis and show that the quantum radiation is non-thermal and evaporation accompanies gravitational collapse.

Quantum superposition principle and gravitational collapse: Scattering times for spherical shells

A quantum theory of spherically symmetric thin shells of null dust and their gravitational field is studied. In Nucl. Phys. B603, 555 (2001), it has been shown how superpositions of quantum states with different geometries can lead to a solution of the singularity problem and black hole information paradox: the shells bounce and re-expand and the evolution is unitary. The corresponding scattering times will be defined in the present paper. To this aim, a spherical mirror of radius ${R}_{m}$ is introduced. The classical formula for scattering times of the shell reflected from the mirror is extended to quantum theory. The scattering times and their spreads are calculated. They have a regular limit for ${R}_{m}\ensuremath{\rightarrow}0$ and they reveal a resonance at ${E}_{m}={c}^{4}{R}_{m}/2G$. Except for the resonance, they are roughly of the order of the time the light needs to cross the flat space distance between the observer and the mirror. Some ideas are discussed of how the construction of the quantum theory could be changed so that the scattering times become considerably longer.

THE QUANTUM GRAVITATIONAL BLACK HOLE IS NEITHER BLACK NOR WHITE

Understanding the end state of black hole evaporation, the microscopic origin of black hole entropy, the information loss paradox, and the nature of the singularity arising in gravitational collapse — these are outstanding challenges for any candidate quantum theory of gravity. Recently, a midisuperspace model of quantum gravitational collapse has been solved using a lattice regularization scheme. It is shown that the mass of an eternal black hole follows the Bekenstein spectrum, and a related argument provides a fairly accurate estimate of the entropy. The solution also describes a quantized mass–energy distribution around a central black hole, which in the WKB approximation, is precisely Hawking radiation. The leading quantum gravitational correction makes the spectrum non-thermal, thus providing a plausible resolution of the information loss problem.

Essay: The Quantum Gravitational Black Hole Is Neither Black Nor White

Understanding the end state of black hole evaporation, the microscopic origin of black hole entropy, the information loss paradox, and the nature of the singularity arising in gravitational collapse - these are outstanding challenges for any candidate quantum theory of gravity. Recently, a midisuperspace model of quantum gravitational collapse has been solved using a lattice regularization scheme. It is shown that the mass of an eternal black hole follows the Bekenstein spectrum, and a related argument provides a fairly accurate estimate of the entropy. The solution also describes a quantized mass-energy distribution around a central black hole, which in the WKB approximation, is precisely Hawking radiation. The leading quantum gravitational correction makes the spectrum non-thermal, thus providing a plausible resolution of the information loss problem.

Black hole thermodynamics without a black hole?

In the present paper we consider, using our earlier results, the process of quantum gravitational collapse and argue that there exists the final quantum state when the collapse stops. This state, which can be called the “no-memory state”, reminds the final “no-hair state” of the classical gravitational collapse. Translating the “no-memory state” into classical language we construct the classical analogue of quantum black hole and show that such a model has a topological temperature which equals exactly the Hawking's temperature. Assuming for the entropy the Bekenstein–Hawking value we develop the local thermodynamics for our model and show that the entropy is naturally quantized with the equidistant spectrum S+ γ 0 N. Our model allows, in principle, to calculate the value of γ 0. In the simplest case, considered here, we obtain γ 0=ln2.

TOWARDS A THEORY OF QUANTUM BLACK HOLES

We describe some specific quantum black hole model. It is pointed out that the origin of a black hole entropy is the very process of quantum gravitational collapse. The quantum black hole mass spectrum is extracted from the mass spectrum of the gravitating source. The classical analog of quantum black hole is constructed.

Singularities in a scalar field quantum cosmology.

The quantum theory of a spatially flat Friedmann-Robertson-Walker universe with a massless scalar field as the source is further investigated. The classical model is singular and in the framework of a genuine canonical quantization (Arnowitt-Deser-Misner formalism) a discussion is made of the cosmic evolution, particularly of the quantum gravitational collapse problem. It is shown that in a matter-time gauge such that time is identified with the scalar field the classical model is singular either at t=-\ensuremath{\infty} or at t=+\ensuremath{\infty}, but the quantum model is nonsingular. The latter behavior disproves a conjecture according to which quantum cosmological singularities are predetermined on the classical level by the choice of time. \textcopyright{} 1996 The American Physical Society.

Quantum gravitational collapse of a scalar field and the wave function of black hole decay.

We develop a quantum description of spherically symmetric gravitational collapse of a massless scalar field. The canonical quantization procedure is applied to a minisuperspace model in which the four-metric and scalar field variables are restricted to a self-similar functional form. Our main purpose is to propose a mechanism of black hole decay in terms of a time evolution of the wave function defined on the minisuperspace. For the self-similar classical dynamics there exists a one-parameter family of solutions for the Einstein-scalar equations, and the Hamiltonian turns out to play the role of the critical parameter which separates the supercritical solution corresponding to a black hole formation from the subcritical one corresponding to a wave reflection to infinity. We derive a set of the eigenfunctions of the quantum Hamiltonian operator, which is interpreted to be the quantum version of the supercritical and subcritical solutions. One of the metric components is also treated as a quantum operator which does not commute with the Hamiltonian operator. The expansion of the eigenfunction of the metric operator in terms of the Hamiltonian eigenfunctions motivates us to introduce the superposition principle and the time-dependent Schr\odinger equation which lead to the uncertainty of the Hamiltonian eigenvalue. Then we study the time evolution of the initial black hole state, which is chosen to be one of the supercritical Hamiltonian eigenstates. We arrive at the conclusion that the time evolution toward black hole decay is essentially due to the breakdown of orthogonality of the Hamiltonian eigenfunctions: The quantum black hole behaves like a wave packet written by a superposition of the various subcritical states. The localized structure of the black hole wave packet begins to spread as each subcritical state evolves with time according to the Schr\odinger equation. We can estimate the decay time and find the final behavior of the wave function describing an outgoing flux of scalar waves observable at future null infinity.

Erratum: Causality violation and the weak energy condition

A simple self gravitating system --- a thin spherical shell of charged pressureless matter --- is naively quantized as a test case of quantum gravitational collapse. The model is interpreted in terms of an inner product on the positive energy states. An S-matrix is constructed describing scattering between negatively and positively infinite radius.

Quantum gravitational collapse of a charged dust shell.

A simple self-gravitating system---a thin spherical shell of charged pressureless matter---is naively quantized as a test case of quantum gravitational collapse. The model is interpreted in terms of an inner product on the positive energy states. An $S$ matrix is constructed describing scattering between negatively and positively infinite radii.